;-NRLF 


D    E    551    773 


m 


M  E  T  H  O  D  S 


FOR   THE 


COMPUTATION  FROM  DIAGRAMS 


OF 


PKELIMINAKY  AND  FINAL  ESTIMATES 


OF 


KAILWAY    EAKTHWORK, 


WITH   DIAGRAMS 


GIVING  QUANTITIES  ON  INSPECTION  TO  THE  NEAREST  CUBIC  YARD,  FOR  BOTH  REGULAR  AND  IRREGULAR 

SECTIONS,  DIRECT  FROM  ORDINARY  FIELD-NOTES. 


BY    ARTHUR    M.   WELLINGTON, 

CIVIL   ENGINEER. 


PART  IL— PLATES. 


NEW   YORK: 

D.    APPLETON    AND    COMPANY,    549    &    551    BROADWAY. 

1874. 


ENTERED,  according  to  Act  of  Congress,  in  the  year  1874,  by 

D.  APPLETON    &   COMPANY, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


LIST    OF   PLATES. 


I.—  DIAGRAM    OF    CROSS-SECTIONS,    ROAD-BED    14,    SLOPES    If    TO    1. 
II.—         "  «  « 

III.—        "  «  « 

* 

IV.—  «  « 


15j          « 

1* 

TO 

1. 

18, 

n 

TO 

1. 

20,          « 

u 

TO 

1. 

18,          " 

ii 

TO 

1. 

18, 

i 

TO 

1. 

VI.  —        "  «  « 

VII.—  DIAGRAM  OF  SIDE-HILL  CROSS-SECTIONS, 

ROAD-BEDS  12,  14,  15,  16,  18,  20,  SLOPES  If  TO  1, 
ROAD-BED  18,  SLOPES  1J  TO  1  AND  1  TO  1. 

VIII.—  DIAGRAM  OF  TRIANGULAR  PRISMS. 

t  DIAGRAM  OF  PRISMOIDAL  CORRECTION. 
IX.—  )  "     CORRECTION  ON  CURVES. 

'  "     SLOPE-STAKES,  ROAD-BED  12,  SLOPES  1^  TO  1. 

X.—  DIAGRAM  FOR  COMPUTATION  BY  HENCK'S  FORMULA, 
ROAD-BED  18,  SLOPES  1£  TO  1. 

XL—  DIAGRAMS   FOR  PRELIMINARY  ESTIMATES^  SLOPES  If  TO  1. 
XII.—          "  "  "  "          1  TO  1  AND  li  TO  1. 


TABLE   OF  REFERENCE. 


THE  table  below  is  added  to  facilitate  reference  to  the  text,  or  to  render  frequent  reference  unnecessary.  The  third, 
fourth,  and  fifth  columns  give  the  quantities  on  each  of  the  plates  which  are  represented  by  the  vertical,  inclined, 
and  horizontal  lines  respectively,  and,  by  interpolating  the  words  in  parentheses  below,  may  be  made  substantially 
equivalent  to  the  rule  for  use  given  in  the  text.  Thus,  for  the  Diagram  of  Cross-Sections,  read  as  follows : 

"  (Take  the)  vertical  line  representing  width  of  section  on  top,  (and  follow  up  to  the)  inclined  line  representing 
the  centre-height.  The  horizontal  lines  give  quantity  sought  in  cubic  yards." 

The  general  rule  for  the  use  of  every  one  of  the  diagrams  in  the  table  may  be  similarly  read  oft' by  the  interpolation 
of  the  same  words. 

The  remaining  columns  of  the  table  give  references  to  the  text  for  the  formulae,  and  a  few  of  the  rules,  etc.,  which  it 
may  be  most  frequently  necessary  to  consult.  For  more  detailed  references,  the  table  of  contents  in  the  text  must  be 
consulted. 


PLATE. 

DIAGRAM  OF  — 

VERTICAL 
LINKS 
represent— 

INCLINED 
LINES 
represent  — 

HORIZONTAL 
LINES 
give  Quantity 
sought  in- 

FORMULA. 

GENERAL 

KULE  FOR 

Usu. 

Indirect 
Applica'ns 
to  other 
road-beds. 

When  given 
Dimensions 
exceed  limits 
of  Diagram. 

MISCELLANEOUS  RULES. 

equa.          pa£e  par.  page 

par.    page 

par.     page 

par.  page. 

I.  to  VI. 

Cross-Sections. 

Width  of  Sec- 
tion on  top. 

Centre-Height. 

Cubic  Yards. 

(5),              16 

21,    20 

105,     99 

22,       23 
23,       25 

To   reduce  to   Level 
Section. 

24,      26 

VII. 

Side  -  Hill  Cross-Sec- 
tions. 

it          it 

tt           tt 

ti         tt 

(7)  to  (9),  29 

30,    32 

107,   102 

VIII. 

Triangular  Prisms. 

Horizontal  di- 
mension.* 

Vertical  dimen- 
sion.* 

tt         ti 

(19),          46 

61,   40 

(General) 

62,       47 

Special    Rules    for 
Computation. 

62,     47 

IX. 

Prismoidal     Correc- 
tion. 

Width  of  Sec- 
tion on  top. 

Centre-Height. 

u            It 

(16),          38 

43,   43 

108,  102 

46,       46 

Method  of  Centre-  ( 
Heights.             \ 

41,     42 
46,     44 

it 

Correction  on  Curves 

it         ii 

Differ'nce  of  dis- 
tances out. 

Feet  and  tenths. 

(29),          77 

82,    79 

(General) 

For  Sidings  and  Bor- 
row-Pits. 

84-87,  81 

" 

ti                it 

Solidity    for 
Section. 

u        ii 

Cubic  Yards. 

(32),          78 

83,    80 

(  General) 

H 

Slope-Stakes. 

Centre-heig'tg 

Surface-Slope. 

Feet  and  tenths. 

(34),  (86),  85 

91,   86 

110,  104 

Side-Hill  Sections. 

132,    138 

X. 

Compt'n  by  Henck's 
Formula. 

Width  of  Sec- 
tion on  top. 

Centre-Height. 

Cubic  Yards. 

(22)to(24),66 

71,   67 

109,  103 

72,       69 
73,      70 

Side-Hill  and  Irregu- 
lar Earthwork. 

74-76,71 

XI.  &  XII. 

Prelim.  Est.,  No.  1. 

Centre-h'ts.f 

Surface-Slope. 

it        it 

(38),          90 

96,    90 

(  Gen'oTj^ 

94,      89 

Use  of  Odometer. 

97,     92 

"          "      No.  2. 

ti        tt  i 

ti          it 

it        u 

(36),  (37),  88 

93,   88 

(GerSalft 

94,       89 

it     tt        it 

94,     89 

"          "      No.  3. 

C 

u          u 

Coefficient. 

(89),          96 

104,   97 

(General) 

"      No.  4. 

Cubic  Yards. 

Coefficient. 

Cubic  Yards. 

(40),          96 

104,   98 

'  General) 

»  Or  nice  verta. 


t  To  intersection  of  side-slopes. 


Roles  for  application  to  other  side-slopes,  par.  Ill,  page  104. 


S  See  par.  103,  p.  96. 


PLATE    I. 


OF 


0 
5B 
> 

K 
o 


X 

o 

01 
w 


M 
O 

M 

6 

2 
w 


TJ 

r 


PLATE    II. 

PIAGRAM   OF  CROSS   SECTIONS. 


TO     1, 


O 
X 


X 
o 

co  ._ 

w  TJ 

-w  r 

w  > 

H  H 

o  PI 

g  s 


PLATE   III. 

PIAGRAM   OF  CROSS   SECTIONS.       18;     i  ^   TO    i, 


o 

JD 


o 
w 

M 


13 

r 


m  r 

H  n 

o 

Z  I-H 


00 


PLATE   IV. 

plAGRAM     OF    jDROSS     ^ECTIONS.         2O;       1  ^     TO      1  . 


O  ' 


o 
w 


tn 
0 


2      H 


to 

o 


PLATE   V. 

DIAGRAM   OF  CROSS   SECTIONS.       18;     i^   TO    i. 


o 

X 


so 
o 

en 
w 

"TO 

B 

n 

H 

O 
2 
w 


TJ 

r 

> 

H 

n 


PLATE   VI. 

DIAGRAM   OF   CROSS   SECTIONS.       18;     i    TO    i. 


"73 

»-« 

> 

O 
5D 

> 
* 

O 


o 

in 


*Tfl 

m 
n 


r 

H 
P] 


g     r 


00 


H 

C 


o 
u 
cd 

z 
o 

I— 

LJ 

_l 
Q. 
O. 
< 

O 

iff 

CC 
O 

^ 


UJ 

O 


o 

h- 

o 


.  m 


UJ 
Q 


PLATE   VII. 

DIAGRAMS   OF   SIDE    HILL   CROSS   SECTIONS. 


D 

33 


CD 

o 


M 


r 
r 


53 
O 

CO 

CO 


n 
n 
•j 

o 

2 


r 

> 

H 
tn 


o 

o 

h- 

CD 


CD 

O 
UJ 

Z 
CD 

CO 

UJ 
Q 


PLATE  VIII. 

DIAGRAM.   OF  TRIANGULAR  PRISMS. 


0 

m 


2  H 

>  PI 

1  < 

r  E 

>  — 


0) 

i 


PLATE    VIII 


DIAGRAM     OF  TRIANGULAR    PRISMS. 


Mr\A/  vnoi/      n    ADDI  rrn\i  a 


PLATE  IX. 

DIAGRAMS    OF    PRISMOIDAL    CORRECTION,     ETC. 


0 

JO 

s 

co 

0 

•*) 


w 
O 

3 

r 

o 


m 
n 

o 

z 


n 


H 

n 


PLATE    IX. 


DIAGRAMS  OF  PRISMOIDAL  CORRECTION,  ac. 


MFW  vnRk    n  APPI  FTDN  »  r.r 


PLATE   X. 

JDlAGRAM     FOR     COMPUTATION     BY     HENCK'S     FORMULA.          l8|      I  ^     TO 


o 
a 


o 

X 


o 

V 
c 


o 

2 


n 
2 
n 


O 
5) 

c: 
r 


TJ 

r 


H 
O 


PLATE  XI. 

DIAGRAMS    FCR     PRELIMINARY     ESTIMATES.          i  ^   TO    i. 


0 
fO 

g 

CO 


0 

a 


a 
w 
r 


5  r 

5     > 


CO 

H 


-J 

rn 
n 


n 


PLATE   XI, 


:  M  rn   HV    A    M  \A/FI  i  i  MCITONI    r  r 


DIAGRAMS  FOR  PRELIMINARY  ESTIMATES, 


NFW  YORK      n.  APPI  FTflN  ft  T.n 


PLATE  XII. 

DIAGRAMS   FOR    PRELIMINARY    ESTIMATES.        i    TO    i ,    AND    1-4  TO    i. 


o 

73 

> 

<n 


p) 

r 

§ 

2 

0  V 

•<  r 

T?  H 

i  PI 

>  X 

H  i— I 

W  HH 


c 


1: 


3 


PLATE  .XII. 


DESIGNED  BY   A.  M.  WELLI  NGTON,  C.  E. 


DIAGRAMS  FOR  PRELIMINARY  ESTIMATES.  1  to  1,  andV4tol 


M  r\A/   VfiDi/       n    A  nn  i 


U.C.BERKELEY  LIBRARIES 


CDM71S13SM 


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